diff --git a/doc/source/whatsnew/v0.20.3.txt b/doc/source/whatsnew/v0.20.3.txt
index c730142450ea64..cbd86ae4c27224 100644
--- a/doc/source/whatsnew/v0.20.3.txt
+++ b/doc/source/whatsnew/v0.20.3.txt
@@ -51,6 +51,7 @@ Indexing
 ^^^^^^^^
 
 - Bug in ``Float64Index`` causing an empty array instead of ``None`` to be returned from ``.get(np.nan)`` on a Series whose index did not contain any ``NaN`` s (:issue:`8569`)
+- Fixed a bug that prevented joining on a categorical MultiIndex (:issue:`16627`).
 
 I/O
 ^^^
diff --git a/doc/source/whatsnew/v0.21.0.txt b/doc/source/whatsnew/v0.21.0.txt
index c4429eef143274..046a6c885bd24b 100644
--- a/doc/source/whatsnew/v0.21.0.txt
+++ b/doc/source/whatsnew/v0.21.0.txt
@@ -100,7 +100,6 @@ Indexing
 
 - When called with a null slice (e.g. ``df.iloc[:]``), the ``.iloc`` and ``.loc`` indexers return a shallow copy of the original object. Previously they returned the original object. (:issue:`13873`).
 - When called on an unsorted ``MultiIndex``, the ``loc`` indexer now will raise ``UnsortedIndexError`` only if proper slicing is used on non-sorted levels (:issue:`16734`).
-- Fixed a bug that prevented joining on a categorical MultiIndex (:issue:`13873`).
 
 
 I/O
diff --git a/pandas/core/indexes/category.py b/pandas/core/indexes/category.py
index d9e0c218bfafc2..d13636e8b43e23 100644
--- a/pandas/core/indexes/category.py
+++ b/pandas/core/indexes/category.py
@@ -560,6 +560,9 @@ def take(self, indices, axis=0, allow_fill=True,
                                            na_value=-1)
         return self._create_from_codes(taken)
 
+    def is_dtype_equal(self, other):
+        return self._data.is_dtype_equal(other)
+
     take_nd = take
 
     def map(self, mapper):
diff --git a/pandas/core/reshape/merge.py b/pandas/core/reshape/merge.py
index 99d9af28ac0191..c8083af8a9fdf2 100644
--- a/pandas/core/reshape/merge.py
+++ b/pandas/core/reshape/merge.py
@@ -1441,13 +1441,9 @@ def _factorize_keys(lk, rk, sort=True):
         rk = rk.values
 
     # if we exactly match in categories, allow us to use codes
-    if isinstance(lk, CategoricalIndex):
-        ldata = lk._data
-    else:
-        ldata = lk
     if (is_categorical_dtype(lk) and
             is_categorical_dtype(rk) and
-            ldata.is_dtype_equal(rk)):
+            lk.is_dtype_equal(rk)):
         return lk.codes, rk.codes, len(lk.categories)
 
     if is_int_or_datetime_dtype(lk) and is_int_or_datetime_dtype(rk):
diff --git a/pandas/tests/test_join.py b/pandas/tests/test_join.py
index 5d29c5355f8806..215ad21940f4a2 100644
--- a/pandas/tests/test_join.py
+++ b/pandas/tests/test_join.py
@@ -1,11 +1,11 @@
 # -*- coding: utf-8 -*-
 
 import numpy as np
-from pandas import Index
+from pandas import Index, DataFrame, Categorical, merge
 
 from pandas._libs import join as _join
 import pandas.util.testing as tm
-from pandas.util.testing import assert_almost_equal
+from pandas.util.testing import assert_almost_equal, assert_frame_equal
 
 
 class TestIndexer(object):
@@ -196,20 +196,38 @@ def test_inner_join_indexer2():
 
 def test_merge_join_categorical_multiindex():
     # From issue 16627
-    import pandas as pd
-    a = {'Cat1': pd.Categorical(['a', 'b', 'a', 'c', 'a', 'b'],
-                                ['a', 'b', 'c']),
+    a = {'Cat1': Categorical(['a', 'b', 'a', 'c', 'a', 'b'],
+                             ['a', 'b', 'c']),
          'Int1': [0, 1, 0, 1, 0, 0]}
-    a = pd.DataFrame(a)
+    a = DataFrame(a)
 
-    b = {'Cat': pd.Categorical(['a', 'b', 'c', 'a', 'b', 'c'],
-                               ['a', 'b', 'c']),
+    b = {'Cat': Categorical(['a', 'b', 'c', 'a', 'b', 'c'],
+                            ['a', 'b', 'c']),
          'Int': [0, 0, 0, 1, 1, 1],
          'Factor': [1.1, 1.2, 1.3, 1.4, 1.5, 1.6]}
-    b = pd.DataFrame(b).set_index(['Cat', 'Int'])['Factor']
+    b = DataFrame(b).set_index(['Cat', 'Int'])['Factor']
 
-    c = pd.merge(a, b.reset_index(), left_on=['Cat1', 'Int1'],
-                 right_on=['Cat', 'Int'], how='left')
+    c = merge(a, b.reset_index(), left_on=['Cat1', 'Int1'],
+              right_on=['Cat', 'Int'], how='left')
     d = a.join(b, on=['Cat1', 'Int1'])
     c = c.drop(['Cat', 'Int'], axis=1)
-    assert_almost_equal(c, d)
+    assert_frame_equal(c, d)
+
+    a = {'Cat1': Categorical(['a', 'b', 'a', 'c', 'a', 'b'],
+                             ['b', 'a', 'c'],
+                             ordered=True),
+         'Int1': [0, 1, 0, 1, 0, 0]}
+    a = DataFrame(a)
+
+    b = {'Cat': Categorical(['a', 'b', 'c', 'a', 'b', 'c'],
+                            ['b', 'a', 'c'],
+                            ordered=True),
+         'Int': [0, 0, 0, 1, 1, 1],
+         'Factor': [1.1, 1.2, 1.3, 1.4, 1.5, 1.6]}
+    b = DataFrame(b).set_index(['Cat', 'Int'])['Factor']
+
+    c = merge(a, b.reset_index(), left_on=['Cat1', 'Int1'],
+              right_on=['Cat', 'Int'], how='left')
+    d = a.join(b, on=['Cat1', 'Int1'])
+    c = c.drop(['Cat', 'Int'], axis=1)
+    assert_frame_equal(c, d)